Global dynamics of a selection model for the growth of a population with genotypic fertility differences

A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah     

Global analysis of a model of plasmid-bearing,plasmid-free competition in a chemostat with inhibitions

A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat was proposed in a paper of Stephanopoulis and Lapidus. The model was in the form of a system of nonlinear ordinary differential equations. Such models were relevant to commercial production by genetically altered organisms in continuous culture. The analysis there was local. The rigorous global analysis was done in a paper of Hsu, Waltman and Wolkowicz in the case of the uninhibited specific growth rates. This paper provides a mathematically rigorous analysis of the global asymptotic behavior of the governing equations in the cases of combinations of inhibited and uninhibited specific growth rates.Research Supported by the National Council of Science, Republic of China     

Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

A model of competition in the chemostat with an inhibitor is combined with a model of competition in the chemostat between plasmid-bearing and plasmid-free organism to produce a model that more closely approximates the way chemostat-like devices are used in biotechnology. The asymptotic behavior of the solutions of the resulting system of nonlinear differential equations is analyzed as a function of the relevant parameters. The techniques are those of dynamical systems although perturbation techniques are used when the parameter reflecting plasmid-loss is small.Research Supported by National Council of Science, Republic of ChinaResearch Supported by National Science Foundation Grant MCS 9204490     

1,25-Dihydroxy vitamin D2 induces leukemia cell differentiation

This work supported in part by the NIH (USPHS), Council for Tobacco Research, American Institute for Cancer Research, and the Cornell Consolidated and Cornell Biotechnology Program which is sponsored by the New York State Science and Technology Foundation, a consortium of industries, the US Army Research Office and the National Science Foundation.     

A predator prey model with age structure

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects its fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and destabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the maturation periodm of the predator. The main result of the paper is that for a broad class of maturation functions positive equilibria are either unstable for smallm or are destabilized asm decreases to zero. This is in contrast to the usual rule of thumb that increasing (not decreasing) delays in growth rate responses cause instabilities.Research supported by National Science Foundation Grant No. MCS-7901307-01Research supported by National Scholarship for Study Abroad No. EDN/S-59/80 from the government of India     

Bifurcation analysis of a nonlinear field model of regeneration

The analysis of bifurcating solutions in the Totafurno and Trainor [23] model of supernumerary limb production in salamanders is re-examined using the symmetry analysis developed by Totafurno [22]. In particular, we show analytically that the appearance of field solutions possessing 2 and 4 singularities (the 2- and 4-centered solutions, respectively) also correspond to true bifurcations with reduced symmetries, just as had been previously found for a solution to the field equations not possessing such singularities (the twist solution). While the results have significance primarily for the biological problem, this work serves as an instructive example of the application of symmetry groups to the bifurcation analysis of nonlinear field equations arising from a variational principle. The relationship between the solutions of the nonlinear equations and the corresponding linear equations is discussed.Supported by the National Sciences and Engineering Research Council and the Medical Research Council of CanadaTo whom correspondence should be sent     

A parameter identification problem arising from a model of canalicular bile formation

We develop a simple mathematical model for bile formation and analyze some features of the model that suggest the design for future physiological experiments. The mathematical model results in a boundary value problem for a system of functional differential equations depending on several physical parameters. From the observability of the boundary values we can identify, both qualitatively and quantitatively, some of these physical parameters. This identification then suggests physical experiments from which one could infer some of the bile transport phenomena that are not, at present, directly observable. The mathematical parameter identification problem is solved by converting the boundary value problem to a transition time problem for a quadratic system of ordinary differential equations on the plane where we are able to employ some special properties of quadratic systems in order to obtain a solution.The author was supported by the Air Force Office of Scientific Research and the National Science Foundation under the grants AF-AFOSR-89-0078 and DMS-9022621The author was supported by National Institutes of Health under grant number R37 DK-27623     

The minimisation of random events in the search for group structure

Summary An iterative species ranking and agglomerative clustering technique has been described. Its objectives were the minimisation of miselassification due to random species. occurrence and the demonstration of the changing role of specles in pattern formation.This work was supported by a grant from the National Science and Engineering Research Council of Canada.     

Global analysis of competition for perfectly substitutable resources with linear response

We study a model of the chemostat with two species competing for two perfectly substitutable resources in the case of linear functional response. Lyapunov methods are used to provide sufficient conditions for the global asymptotic stability of the coexistence equilibrium. Then, using compound matrix techniques, we provide a global analysis in a subset of parameter space. In particular, we show that each solution converges to an equilibrium, even in the case that the coexistence equilibrium is a saddle. Finally, we provide a bifurcation analysis based on the dilution rate. In this context, we are able to provide a geometric interpretation that gives insight into the role of the other parameters in the bifurcation sequence. Funding was provided by the National Science Foundation-funded ADVANCE Institutional Transformation Program at New Mexico State University, fund # NSF0123690. Research partially supported by the Natural Science and Engineering Research Council of Canada.     

A generalized diffusion model for growth and dispersal in a population

A reaction-diffusion model is presented in which spatial structure is maintained by means of a diffusive mechanism more general than classical Fickian diffusion. This generalized diffusion takes into account the diffusive gradient (or gradient energy) necessary to maintain a pattern even in a single diffusing species. The approach is based on a Landau-Ginzburg free energy model. A problem involving simple logistic kinetics is fully analyzed, and a nonlinear stability analysis based on a multi-scale perturbation method shows bifurcation to non-uniform states.Part of this work was done while at the Mathematical Institute, Oxford University as a Senior Visiting Fellow supported by the Science Research Council of Great Britain under grant GR/B31378     

Global stability of a predator-prey system

In this paper we derive a result to ensure the global stability of a predator-prey system. The method used is quite general and may have applications to other situations.Works were partially supported by the National Science Council of the Republic of China     

The Use of the Microcomposter to Study the Dynamics of a Mini-Ecosystem

In this activity, students learn about the important topic of invasive species, specifically Zebra Mussels. Students role-play different characters in a real-life situation: the trial of the Zebra Mussel for unlawful disruption of the Great Lakes ecosystem. Students will also learn about jurisprudential inquiry by examining the trial process. This activity will reinforce important knowledge and skills underscored in the Life Science and Science in Personal and Social Perspectives Standards in the National Science Education Standards (National Research Council 1996).     

Localization of the Extracellular Matrix Protein SC1 to Synapses in the Adult Rat Brain

Extracellular matrix molecules play important roles in neural developmental processes such as axon guidance and synaptogenesis. When development is complete, many of these molecules are down-regulated, however the molecules that remain highly expressed are often involved in modulation of synaptic function. SC1 is an example of an extracellular matrix protein whose expression remains high in the adult rat brain. Confocal microscopy revealed that SC1 demonstrates a punctate pattern in synaptic enriched regions of the cerebral cortex and cerebellum. Higher resolution analysis using electron microscopy indicated that SC1 localizes to synapses, particularly the postsynaptic terminal. SC1 was also detected in perisynaptic glial processes that envelop synapses. This work was supported by the National Science and Engineering Research Council of Canada.     

Trgrps — an interactive algorithm for group recogniton with an example from spartinetea

Summary TRGRPS can detect groups or signal if discrete groups cannot be found in a sample. The present paper elaborates on the concepts, describes the algorithm and provides illustrations from syntaxonomy. A computer program (TRGRPS.BAS) is available from the author upon request.Contribution from the Working Group for Data Processing in Phytosociology, International Society for Vegetation Science. For nomenclature of species see Lausi, Beeftink & Kortekaas (1975).The research project, from which this paper summarizes partial results, is supported by a National Research Council of Canada grant. Computer time was provided by the University of Western Ontario.     

Analysis of a model for antagonistic muscles

In the present work a linear model for a pair of antogonistic muscles is analysed. Each constituent muscle in this model is identical to ones considered previously (Stein and Ouztöreli, 1976). Analytical properties of the antagonistic muscles and dynamics of the system are described and some numerical results are discussed. The natural modes of the system are determined by a fourth order polynomial, which most commonly has one pair of conjugate complex roots and two negative real roots. The filtering of neural inputs through the active state properties of the muscle increases the order of the system to fifth order for these inputs.This work was partly supported by the National Scientific and Engineering Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MT-3307 through the University of Alberta     

Beneficial effects of activated charcoal on plant tissue and organ cultures

Summary Addition of activated charcoal to the medium for plant tissue cultures improves growth by adsorbing toxic metabolites. This research was supported in part by the National Science Council, Republic of China     

Optimal HIV treatment by maximising immune response

We present an optimal control model of drug treatment of the human immunodeficiency virus (HIV). Our model is based upon ordinary differential equations that describe the interaction between HIV and the specific immune response as measured by levels of natural killer cells. We establish stability results for the model. We approach the treatment problem by posing it as an optimal control problem in which we maximise the benefit based on levels of healthy CD4+ T cells and immune response cells, less the systemic cost of chemotherapy. We completely characterise the optimal control and compute a numerical solution of the optimality system via analytic continuation.Research supported by the Natural Science and Engineering Research Council (NSERC) and the Mathematics of Information Technology and Complex Systems (MITACS) of Canada     

The relationship between the activation state of sucrose-phosphate synthase and the rate of CO2 assimilation in spinach leaves

The relationship between the gas-exchange characteristics of spinach (Spinacia oleracea L.) leaves and the activation state of sucrose-phosphate synthase was examined at different intercellular partial pressures of CO₂ at two different photon flux densities. There was a strong positive correlation between the activation state of sucrose-phosphate synthase and the assimilation rate. The relationship was the same at both photon flux densities, indicating that the activation state of the enzyme is determined by a product of carbon assimilation, rather than directly by light.Abbreviations A assimilation rate for CO₂ - p _i intercellular CO₂pressure - PFD photon flux density - SPS sucrose-phosphate-synthase - Glc6P glucose-6-phosphate - Fru6P fructose-6-phosphate A.B. was the recipient of a visiting fellowship from the National Research Council of the Italy. This work was also supported by the Science and Engineering Research Council and the Agricultural and Food Research Council, UK.     

The dye-exclusion test for cell viability: Persistence of differential staining following fixation

Summary A method is described whereby the differential staining of viable and nonviable unfixed cells, as observed by the dye-exclusion method, can be reproduced in glutaraldehyde-fixed preparations by staining with alcian blue. The results suggest that the differential staining is due, at least in part, to structural differences that are retained following aldehyde fixation. This work was supported by grants from the National Cancer Institute of Canada and the National Research Council of Canada. Recipient of a Research Studentship from the National Cancer Institute of Canada.     

The discrimination of polarized light by the tarantula

Summary The present experiment compared the establishment of a position habit and three subsequent response shifts with and without discriminative stimuli. The discriminative stimuli employed were (a) 90° and 180° polarization patterns and (b) high and low intensity levels. A significant difference (0.05) was found between the running time performance of the polarization discrimination group and the uniform illumination and bright-dark discrimination groups. No similar difference was found with errors as the dependent measure, and no significant between group differences were found during the response shifts. The conclusion was drawn that the extra-ocular hypothesis could not account for the significant difference.This paper is taken from a Master's Thesis submitted to the Florida State University by the senior author, under the direction of the junior author, in partial fulfillment of the requirements for the degree of Master of Science. A portion of this paper was presented at the 1965 meeting of the American Psychological Association.This research was partially supported by a grant from the Florida State University Research Council. The statistical analyses were made possible in part by a National Science Foundation grant (# GP 671) to the Florida State University Computation Center. The authors are indebted to Dr. F. J. King, Institute of Human Learning, Florida State University, for his contribution to the data analysis.